Yes, there is a stipulation that they will act despondently and strangely 1 in 20 rounds. But mostly they are immortal killing machines. Sometimes immortal killing machines infested with rot grubs.

That said, the idea of a deathless opponent, one who you can communicate with, one that you cannot destroy has interest. Especially since they can be created from extant creatures in your campaign with a bestow curse and a wish.